I was born and raised in and around ABQ. Honestly, you'll have the best luck either searching the bosque, or head east on interstate 40 into the east mountains (worth the trip IMHO).
If you do go east on I40, stay on the interstate for about 20-30 minutes and take the Cedar Crest/Tijeras exit, then head north on highway 14 until you pass a shell gas station on the right. From there you can either hang a left and go up the crest road to search for pieces (lots of places to pull of the road and lots of trails to go hiking). You can also continue on North 14, and pass East Mountain High School, which will be on the left (where I went to HS) and there will be a lot of different pieces just a short distance off and around the road. Please do note that the east mountains are at about 7500ft though, while ABQ is closer to 5000ft above sea level.
I'm not as familiar with the bosque, but anything you find would most likely have been carried by the river, so there are possible contamination issues you may face.
NM has a plethora of cholla wood, which looks beautiful in tanks! GL with your search!
I hope to see pics if you find anything!